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<p>For a colour cluster <span class="math"><em>C</em> = (C₁, C₂, C₃, …, C_ℓ)</span>, where <span class="math">C_<em>i</em></span> is a colour class such that <span class="math">∣C_<em>i</em>∣ = <em>r</em>_<em>i</em></span>, a positive integer, we investigate two types of simple connected graph structures <span class="math"><em>G</em>₁^<em>C</em></span>, <span class="math"><em>G</em>₂^<em>C</em></span> which represent graphical embodiments of the colour cluster such that the chromatic numbers <span class="math"><em>χ</em>(<em>G</em>₁^<em>C</em>) = <em>χ</em>(<em>G</em>₂^<em>C</em>) = ℓ</span> and <span class="math">$\min\{\varepsilon(G^{C}_1)\}=\min\{\varepsilon(G^{C}_2)\} =\sum\limits_{i=1}^{\ell}r_i-1$</span>, and <span class="math"><em>ɛ</em>(<em>G</em>)</span> is the size of a graph <span class="math"><em>G</em></span>. In this paper, we also discuss the chromatic Zagreb indices corresponding to <span class="math"><em>G</em>₁^<em>C</em></span>, <span class="math"><em>G</em>₂^<em>C</em></span>.</p>